Double-Inversion Mechanisms of the X− + CH3Y [X,Y = F, Cl, Br, I] SN2ReactionsIstvan Szabo and Gabor Czako*

Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, Eotvos University, P.O. Box 32, H-1518 Budapest 112,Hungary

*S Supporting Information

ABSTRACT: The double-inversion and front-side attack transition states as well as theproton-abstraction channels of the X− + CH3Y [X,Y = F, Cl, Br, I] reactions arecharacterized by the explicitly correlated CCSD(T)-F12b/aug-cc-pVTZ(-PP) level oftheory using small-core relativistic effective core potentials and the corresponding aug-cc-pVTZ-PP bases for Br and I. In the X = F case the double-inversionclassical(adiabatic) barrier heights are 28.7(25.6), 15.8(13.4), 13.2(11.0), and 8.6(6.6)kcal mol−1 for Y = F, Cl, Br, and I, respectively, whereas the barrier heights are in the40−90 kcal mol−1 range for the other 12 reactions. The abstraction channels are alwaysabove the double-inversion saddle points. For X = F, the front-side attackclassical(adiabatic) barrier heights, 45.8(44.8), 31.0(30.3), 24.7(24.2), and 19.5(19.3)kcal mol−1 for Y = F, Cl, Br, and I, respectively, are higher than the correspondingdouble-inversion ones, whereas for the other systems the front-side attack saddle pointsare in the 35−70 kcal mol−1 range. The double-inversion transition states have XH···CH2Y

− structures with Cs point-group symmetry, and the front-side attack saddle points have either Cs (X = F or X = Y) or C1symmetry with XCY angles in the 78−88° range. On the basis of the previous reaction dynamics simulations and the minimumenergy path computations along the inversion coordinate of selected XH···CH2Y

− systems, we suggest that the double inversionmay be a general mechanism for SN2 reactions.

1. INTRODUCTION

The back-side attack Walden inversion mechanism of thebimolecular nucleophilic substitution (SN2) reactions is one ofthe best-known stereospecific reaction pathways in organicchemistry. The simplest SN2 reactions are X− + CH3Y type,where X and Y are halogens (F, Cl, Br, I). Walden inversionoccurs when X− attacks the back side of CH3Y, the system goesthrough a central transition state, and the umbrella motion ofthe CH3 group inverts the configuration around the carboncenter while a new CX bond forms and the CY bond breaks,thereby resulting in XCH3 + Y− products (Figure 1). There isalso a less-known front-side attack retention pathway (Figure1), which goes over a high-energy barrier.1−6 Very recently, wehave uncovered a new double-inversion mechanism for the F−

+ CH3Cl SN2 reaction, in which a proton-abstraction-inducedinversion is followed by a second inversion, thereby resulting inretention of configuration, as shown in Figure 1.6 The first stepof the double inversion is the formation of a XH···CH2Y

−

complex, in which an inversion can occur. Then, either thereaction produces an inverted CH3Y molecule or the firstinversion is followed by a second inversion via the usual [X···CH3···Y]

− transition state, resulting in a CH3X product withretention of the initial configuration. For the F− + CH3Clreaction, we have found a FH···CH2Cl

− transition state (first-order saddle point) of Cs point-group symmetry, in which theCH2Cl

− group is almost planar and FH is in the Cs plane.6 The

electronic energy of this so-called double-inversion transition

state is just above the reactants asymptote by 16.4 kcal mol−1,whereas the classical barrier height of the front-side attack is ashigh as 31.3 kcal mol−1.6 Thus, the double inversion opens a

Received: January 30, 2015Revised: March 6, 2015Published: March 6, 2015

Figure 1. Different mechanisms of the X¯ + CH3Y reactions. Bluebackground denotes an inverted configuration relative to that of thereactant (yellow).

Article

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© 2015 American Chemical Society 3134 DOI: 10.1021/acs.jpca.5b00988J. Phys. Chem. A 2015, 119, 3134−3140

significantly lower energy retention pathway for the F− +CH3Cl reaction than the front-side attack. Reaction dynamicssimulations on an accurate global ab initio analytical potentialenergy surface6 showed that the dominant mechanism of the F−

+ CH3Cl reaction is the back-side attack substitution. At acollision energy of ∼10 kcal mol−1 the double-inversionpathway opens, and this is the mechanism that is responsiblefor retention in the collision energy range of 10−40 kcal mol−1

because the threshold energy of the front-side attack is ∼40 kcalmol−1. Furthermore, at a collision energy of ∼20 kcal mol−1 theHF + CH2Cl

− abstraction channel opens as well. As expected,the reactant’s CH stretching excitation enhances the doubleinversion and the abstraction channel, whereas it does notsignificantly affect the back-side attack reactivity.After revealing this novel double-inversion mechanism for

the F− + CH3Cl reaction an obvious and important questioncomes to everyone’s mind. Is the double inversion a generalpathway for SN2 reactions? In the present study we aim toinvestigate the possibility of double inversion in 16 SN2reactions of the X− + CH3Y type, where X and Y are F, Cl, Br,and I. Six reactions, where the atomic number of X is less thanthat of Y, are exothermic, the six reverse reactions areendothermic, and there are four isoenergetic identity reactions,where X and Y are the same. Many previous theoretical studiesinvestigated the Walden inversion pathway involving the pre-and postreaction ion−dipole complexes and the centraltransition states;7−18 therefore, here we focus on the less-known retention pathways and the abstraction channel. We use

high-level ab initio methods to characterize the double-inversion saddle points as well as the front-side attack transitionstates and the proton-abstraction channels of the previouslymentioned 16 reactions. The present ab initio results provideguidance for future dynamical investigations of the retentionpathways in SN2 reactions.

2. COMPUTATIONAL DETAILS

We have computed the structures and harmonic vibrationalfrequencies of the stationary points using the explicitlycorrelated coupled-cluster singles, doubles, and perturbativetriples CCSD(T)-F12b (ref 19) method with the augmentedcorrelation-consistent polarized valence n-zeta aug-cc-pVnZ [n= D and T] basis sets.20 For Br and I, small-core energy-consistent relativistic effective core potentials and thecorresponding aug-cc-pVnZ-PP [n = D and T] basis sets areused.21 The constrained optimizations, where one of theinternal coordinates is fixed, have been carried out at theCCSD(T)-F12b/aug-cc-pVDZ(-PP) level of theory. Theelectron correlation computations employ the usual frozen-core approach. All computations are performed using the abinitio program package Molpro.22

3. RESULTS AND DISCUSSION

The classical and zero-point energy (ZPE)-corrected adiabaticrelative energies of the double-inversion and front-side attacksaddle points and the HX + CH2Y

− products obtained at the

Figure 2. Classical and zero-point vibrational energy corrected (adiabatic) energies of the double-inversion and front-side attack saddle points andabstraction-channel products (HX + CH2Y

−) relative to the energies of the reactants, X¯(color coded) + CH3Y(columns), obtained at theCCSD(T)-F12b/aug-cc-pVTZ(-PP) level of theory.

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CCSD(T)-F12b/aug-cc-pVTZ(-PP) level of theory are given inFigure 2. In Tables S1−S3 in the Supporting Information (SI)the corresponding aug-cc-pVDZ(-PP) energies are given aswell. The ZPE values and the harmonic vibrational frequenciesof all the stationary points are given in Tables S4−S6 in the SI.The aug-cc-pVDZ(-PP) and aug-cc-pVTZ(-PP) basis sets givethe same relative energies within ∼0.5 kcal mol−1, or in manycases the agreement is much better. This shows the fast basisset convergence of the explicitly correlated F12 method andsuggests that the aug-cc-pVTZ(-PP) basis provides well-converged results with about ±0.1 kcal mol−1 uncertaintyrelative to the complete-basis-set results. For F− + CH3Cl, thebenchmark relative energies are also available,6 obtained by the

focal-point analysis (FPA) approach,23,24 which considersextrapolation to the complete-basis-set limit, electron correla-tion beyond CCSD(T), core electron correlation, and scalarrelativistic effects. The FPA classical barrier heights andreaction endothermicity are 16.4, 31.3, and 29.2 kcal mol−1

(ref 6) for double inversion, front-side attack, and abstraction,respectively, whereas the corresponding CCSD(T)-F12b/aug-cc-pVTZ values are 15.8, 31.0, and 28.7 kcal mol−1. Theseresults suggest that the present relative energies are well withinchemical accuracy (uncertainties <1 kcal mol−1). In the cases ofdouble-inversion barrier height and endothermicity of theabstraction channel, the deviations between the CCSD(T)-F12b/aug-cc-pVTZ and FPA energies are mainly due to the

Figure 3. Structures of the double-inversion saddle points obtained at the CCSD(T)-F12b/aug-cc-pVTZ(-PP) level of theory. The distances and theHbCY angles are given in angstroms and degrees, respectively, where Hb denotes the abstracted hydrogen atom in the Cs plane.

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core electron correlation effects. For front-side attack, the largecore correlation effect is almost canceled by the substantialpost-CCSD(T) correlation and scalar relativistic effects.As Figure 2 shows, the double-inversion barrier heights and

the endothermicity of the abstraction channels of the X− +CH3Y reactions increase as X goes from F to I and decrease asY goes from F to I. Thus, the I− + CH3F reaction has thehighest double-inversion barrier height and abstractionendothermicity, whereas the F− + CH3I reaction has thelowest ones. In all cases the double-inversion saddle point isbelow the HX + CH2Y

− asymptote. This indicates that theproton-inducted inversion, the first step of double inversion,can happen even if the system does not have enough energy tobreak apart to form the HX + CH2Y

− products. The F− +CH3Y reactions have significantly lower classical double-inversion barrier heights of 28.7, 15.8, 13.2, and 8.6 kcalmol−1 for Y = F, Cl, Br, and I, respectively, than the other 12reactions that have barrier heights in the 45−90 kcal mol−1

range. On the basis of these results we can conclude that the F−

+ CH3Cl reaction, where the double-inversion mechanism wasdiscovered,6 is a good candidate for double inversion, but theF− + CH3I reaction might be even better. The special role of F

−

among the halide nucleophiles may be explained by its highproton affinity. Furthermore, the hydrogen-bonded complexeswere only discovered in the entrance channels of the F− +CH3Y reactions.14,25,6,16

For the front-side attack there are only 10 distinct saddlepoints because the forward and backward reactions have thesame transition states. Of course, the barrier heights of thenonidentity X− + CH3Y and Y− + CH3X reactions are differentbecause the same saddle-point energy is relative to differentreactant energies. As Figure 2 shows, some trends can beobserved for the energy order of the front-side attack barrierheights. Similar to the double-inversion, the front-side attackbarrier heights of X− + CH3Y increase as X goes from F to I anddecrease as Y goes from F to I. Among all reactions investigated

Figure 4. Structures of the front-side attack saddle points obtained at the CCSD(T)-F12b/aug-cc-pVTZ(-PP) level of theory. The CX and CYdistances and the XCY angles are given in angstroms and degrees, respectively.

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in this study, the I− + CH3F reaction has the highest front-sideattack barrier (66.8 kcal mol−1), whereas F− + CH3I has thelowest one (19.5 kcal mol−1). For the X− + CH3X identityreactions the front-side attack barrier height increases from F(45.8 kcal mol−1) to Cl (48.6 kcal mol−1) and then decreases asBr (43.9 kcal mol−1) and I (41.5 kcal mol−1).Comparing the double-inversion and front-side attack barrier

heights, we can conclude that in the case of the F− + CH3Y [Y= F, Cl, Br, I] reactions the double-inversion saddle points arewell below the front-side attack ones. Thus, for the four F− +CH3Y systems we can expect retention of configuration atcollision energies below the front-side attack barrier height. Inthe case of the other 12 reactions the double-inversion classicalbarrier heights are higher than the front-side attack ones.The ZPE corrections have substantial effects on the double-

inversion barrier heights and the endothermicity of the proton-abstraction channel, whereas the ZPE effects on the front-sideattack barrier heights are less significant. As Figure 2 shows, theZPE correction decreases the double-inversion barrier heightsby about 2−3 kcal mol−1 for F− + CH3Y and by about 4−6 kcalmol−1 for the other 12 reactions. For the abstraction channels,the ZPE effects are even larger; the adiabatic product relativeenergies are below the classical ones by 3−5 kcal mol−1 for HF+ CH2Y

− and by 5−7 kcal mol−1 for the other 12 systems. TheZPE correction also decreases the front-side attack barriers, butthe effects are only in the 0.2 to 2.1 kcal mol−1 range. Althoughsome of the ZPE effects are large, the adiabatic relative energiesare qualitatively similar to the classical ones.The geometries and the most important structural

parameters of the double-inversion and front-side attack saddlepoints are shown in Figures 3 and 4, respectively. The structuralparameters of the saddle points are also listed in Tables S7 andS8 in the SI and the structures of CH3Y, CH2Y

−, and HX aregiven in Table S9 in the SI. The interested reader can also findthe Cartesian coordinates of the double-inversion and front-side attack saddle points in Tables S10 and S11, respectively, inthe SI. As Figure 3 shows, all double-inversion saddle pointshave Cs point-group symmetry and consist of an XH and aCH2Y

− group. The XH saddle-point distances are slightlystretched relative the isolated HX molecule. The mostsignificant stretching effects of 0.06 to 0.09 Å are seen for theFH distances and for ClH···CH2I

−, where the ClH distance is0.14 Å larger than the bond length of the HCl molecule. In thecase of X = Cl, Br, and I, the structure of the CH2Y

− group isvery similar to that of the free CH2Y

−; for example, the CYdistances are just 0.001 to 0.004 Å shorter at the saddle pointthan in the isolated CH2Y

− if Y = Cl, Br, and I and 0.013 to0.025 Å longer in the case of Y = F. The sole exemption isClH···CH2I

−, where the CI distance is significantly contractedby 0.127 Å. In the case of the FH···CH2Y

− saddle points, thestructure of the CH2Y

− group is significantly distorted, the CYdistances are contracted by 0.062, 0.134, 0.154, and 0.165 Å forY = F, Cl, Br, and I, respectively, and the CH2Y

− group is closeto a planar structure. The similarity of the FHb···CH2Y

− [Y = F,Cl, Br, I] and the ClHb···CH2I

− saddle-point structures is alsoseen in the case of the HbCY angles, which are in the 90−100°range for these five structures, whereas the HbCY angles are inthe 55−65° range for the other 11 systems. The HbC distances,∼1.8 Å, are also similar for the FHb···CH2Y

− and the ClHb···CH2I

− saddle points, whereas the corresponding values are inthe 2.2 to 2.7 Å range for the other reactions. (Among these theshortest values, ∼2.2 Å, are for XHb···CH2F

− [X = Cl, Br, I].)

As Figure 4 shows, at the front-side attack saddle points, twohalogens are connected to the carbon atom and both the CXand CY distances are substantially stretched relative to thecorresponding bond lengths in the isolated methyl-halides.Because both the forward and backward reactions go over thesame front-side attack barrier, six−six saddle-point structuresare the same. The FYCH3

− structures, where Y = Cl, Br, and I,are special because in this case the transition state has Cssymmetry, where four atoms, F, Y, C, and H, are in the Csplane. All of the other systems have saddle-point structureswithout having four atoms in a plane. The identity reactionsalso have Cs point-group symmetry, but here the two identicalhalogens and two hydrogen atoms are out of the plane. TheClBrCH3

−, ClICH3−, and BrICH3

− systems have structuressimilar to the identity reactions; however, because of thedifferent halogen ligands these saddle points have C1 symmetry.The XCY angles are ∼80° if X or Y is F; otherwise, the anglesare ∼85°. These bond angles suggest significant sidewaysscattering, which was found in the case of the front-side attacktrajectories of the F− + CH3Cl reaction.

6 The CY distances arestretched by ∼0.5 Å for the FYCH3

− saddle points relative tocorresponding CY bond lengths in the CH3Y molecules. In thecase of the XYCH3

− saddle points, where X = Cl, Br, and I, theCF, CCl, CBr, and CI distances are about 0.10 to 0.14, 0.14 to0.19, 0.16 to 0.21, and 0.20 to 0.26 Å larger, respectively, thanthe corresponding values for FYCH3

−.The key step of the double-inversion mechanism is the

inversion of the CH2Y− group via a XH···CH2Y

− saddle point.Let us first investigate the inversion of the isolated CH2Y

−

system. The double-well potential energy curves of CH2Y− [Y =

F, Cl, Br, I] along the inversion coordinate are shown in Figure5. The minima correspond to pyramidal equilibrium structures

with Cs symmetry, whereas at the top of the barrier CH2Y− is

planar with C2v symmetry. The inversion classical (adiabatic)barrier heights are 13.2(13.0), 12.4(12.2), 14.3(13.9), and13.8(13.4) kcal mol−1 for Y = F, Cl, Br, and I, respectively, atthe CCSD(T)-F12b/aug-cc-pVDZ(-PP) level of theory, andthe corresponding aug-cc-pVTZ(-PP) values are 13.0(12.8),12.7(12.3), 14.4(14.0), and 13.8(13.4) kcal mol−1. Theserelatively small barriers indicate that a proton-abstraction-induced inversion can happen in the X− + CH3Y systems. Toinvestigate the minimum energy path of the induced inversion,we performed constrained optimizations starting from the

Figure 5. Potential energy curves for CH2Y¯ [Y = F, Cl, Br, I] obtainedby constrained optimizations at the CCSD(T)-F12b/aug-cc-pVDZ(-PP) level of theory. α is defined as the ZCH angle, where Z is adummy atom in the Cs plane with ZCY angle of 90°.

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double-inversion saddle points fixing the α inversion coordinateand relaxing the other internal coordinates. We define angleα(ZCH) using a dummy atom Z in the Cs plane with ZCYangle of 90° and one of the out-of-plane H atoms. Thepotential energy curves as a function of α are given in Figure 6for the F− + CH3Cl, F

− + CH3I, Cl− + CH3I, and Br

− + CH3Brsystems. Reaction dynamics simulations performed recently6

for F− + CH3Cl showed that after F− abstracts a proton, thesystem typically rotates into a double-inversion saddle-point-like configuration, which corresponds to α > 100° in Figure 6.Then, the configuration around the carbon center can invert (αdecreases below 90°) while the FH bond breaks and a CHbond forms. As Figure 6 shows, along this inversion reactionpath the potential energy decreases rapidly apart from a smallbarrier in some cases. These potential energy paths clearly showthat the inversion can occur for various systems; the maindifference is in the energy of the saddle-point-like structurerelative to that of the reactants. For F− + CH3Cl and F− +CH3I, the relative energies go up to about 16 and 8 kcal mol−1,respectively, whereas for Cl− + CH3I and Br

− + CH3Br the ClHand BrH have to climb up to as high as 46 and 62 kcal mol−1.Of course, reaction dynamics simulations should be performedto verify these reaction pathways.

4. SUMMARY AND CONCLUSIONS

Recent reaction dynamics simulations on an analytical ab initiopotential energy surface revealed a novel double-inversionmechanism for the F− + CH3Cl SN2 reaction.6 We also foundan FH···CH2Cl

− double-inversion saddle point, which hassignificantly lower energy than that of the front-side attack

transition state.6 In the present study we performed high-levelexplicitly correlated CCSD(T)-F12b computations with triple-ζbasis sets for 16 reactions of X− + CH3Y type, where X and Yare halogens, and showed that XH···CH2Y

−-type double-inversion saddle points exist for all 16 reactions. The double-inversion barrier heights are the smallest for the X = F systemsand increase as X goes from F to I and decrease as Y goes fromF to I. Thus, the F− + CH3I reaction has the lowest double-inversion classical(adiabatic) barrier height of 8.6(6.6) kcalmol−1, which is about the half of the barrier height of the F− +CH3Cl reaction. For the X− + CH3X identity reactions thedouble-inversion classical(adiabatic) barrier heights are28.7(25.6), 54.8(50.3), 61.9(56.8), and 67.8(62.3) kcal mol−1

for X = F, Cl, Br, and I, respectively. These results demonstratethat the barrier heights in the case of F− nucleophile aresignificantly less than the others. It is also seen that the ZPEcorrections have substantial effects on the double-inversionbarrier heights. The energy levels of the HX + CH2Y

−

abstraction channels are always above the correspondingXH···CH2Y

− saddle points. The front-side attack saddle pointsare above the double-inversion ones for the F− + CH3Y [Y = F,Cl, Br, I] reactions and the reverse holds for the other systems.Thus, the double inversion is likely to play a more importantrole in the SN2 reactions with F− nucleophile.All double-inversion saddle points have Cs point-group

symmetry. The FH···CH2Y− [Y = F, Cl, Br, I] and ClH···CH2I

−

saddle points have similar structures, HbC distances are ∼1.8 Å,and HbCY angles are in the 90−100° range. For the othersystems the HbC separations are larger, 2.2 to 2.7 Å, and theHbCY angles are 55−65°. The front-side attack saddle pointshave Cs symmetry with four atoms, FYCH, in a plane for the

Figure 6. Potential energy paths for the proton-abstraction-induced inversion of selected X¯ + CH3Y (X = F, Cl, Br; Y = Cl, Br, I) reactions obtainedby constrained optimizations at the CCSD(T)-F12b/aug-cc-pVDZ(-PP) level of theory. α is defined as the ZCH angle, where Z is a dummy atom inthe Cs plane with ZCY angle of 90° and H is one of the out-of-plane H atoms. The energies are relative to X¯ + CH3Y(equilibrium).

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FYCH3− [Y = Cl, Br, I] systems, whereas for the other

reactions the saddle-point structures are twisted, resulting Cssymmetry with only two atoms, CH, in the plane for theidentity reactions and C1 symmetry for the XYCH3

− [X/Y =Cl/Br, Cl/I, Br/I] systems. Both the CX and CY distances aresubstantially stretched by 0.5 to 0.8 Å relative to thecorresponding bond lengths in the isolated methyl-halidemolecules. The XCY angles are in the 78−88° range, whichsuggests the dominance of sideways scattering for the front-sideattack reactive collisions.Reaction pathways along the inversion coordinate of the

XH···CH2Y− systems are investigated. On the basis of the

present results and the typical double-inversion trajectoriesfound previously for the F− + CH3Cl reaction, we can concludethat the proton-abstraction-induced inversion, which is the firststep of the double-inversion mechanism, may be a generalmechanism, where first the XH···CH2Y

− system forms adouble-inversion saddle-point-like structure and second theinversion occurs while the XH bond breaks and a new CHbond forms. The present work may inspire and guide futurereaction dynamics studies to investigate the retentionmechanisms in SN2 reactions.

■ ASSOCIATED CONTENT*S Supporting InformationClassical relative energies of the stationary points obtained atthe CCSD(T)-F12b/aug-cc-pVnZ(-PP) [n = D and T] levels oftheory. Structures and harmonic vibrational frequencies of allthe stationary points investigated in this study and Cartesiancoordinates of the double-inversion and front-side attack saddlepoints obtained at the CCSD(T)-F12b/aug-cc-pVTZ(-PP)level of theory. This material is available free of charge viathe Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: czako@chem.elte.hu.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSG.C. was supported by the Scientific Research Fund ofHungary (OTKA, PD-111900) and the Janos Bolyai ResearchScholarship of the Hungarian Academy of Sciences.

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The Journal of Physical Chemistry A Article

DOI: 10.1021/acs.jpca.5b00988J. Phys. Chem. A 2015, 119, 3134−3140

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